Goals from Sofiane Feghouli, Riyad Mahrez and Yacine Brahimi moved Algeria up to 15 points, the only team to have won all their games thus far.
Algeria head coach Christian Gourcuff made two changes to the side that beat Malawi last time out, with Med Lamine Zemmamouche and Saphir Taider replacing Rais M’Bolhi and Nabil Bentaleb respectively, while Bidvest Wits and Ethiopia striker Getaneh Kebede missed the game through suspension.
The hosts put Ethiopia under immense pressure in the opening 10 minutes of the encounter, with Rafik Halliche notably heading just wide.
It was Ethiopia, though, who opened the scoring completely against the run of play in the 22nd minute through Omod Okwory, who picked up the ball near the halfway line before bursting forward and hitting a right-footed effort past the Algerian glove-man.
Ethiopia continued to live dangerously, but Algeria’s finishing also left a lot to be desired in what was in all a frustrating opening half-an-hour for the hosts.
The Fennec Foxes finally found their goal in the 32nd minute as Feghouli latched onto a superb through ball from Riyad Mahrez.
Provider turned scorer nine minutes later as Mahrez curled the ball past Jemal Tassew before Brahimi added a third in first-half stoppage time, hammering home from close range, to give the hosts a 3-1 lead at the interval.
The Walias had their moments in the second half, but it was the home side who did most of the attacking, with Brahimi and Islam Slimani causing all sorts of problems for the Ethiopian defence.
Algeria now head to Mali in search of the perfect qualifying record ahead of next year’s showpiece in Equatorial Guinea.